Aetheris: Topological Astigmatism of Spacetime as a Unified Geometric Framework for Galactic Dynamics, the Hubble Tension, and Cosmic Age

The current Standard Cosmological Model (ΛCDM) relies on unobserved dark components (Dark Matter and Dark Energy) to resolve critical anomalies across disparate cosmic scales. This preprint introduces the Aetheris framework, proposing a fundamental paradigm shift: spacetime is not a perfectly isotropic void, but an elastic, astigmatic medium that exhibits a non-linear topological resistance (shear) in the deep low-acceleration regime (g < 1.2 × 10⁻¹⁰ m/s²). By defining a topological shear tensor (γ = 0.5000) and an exponential decay factor (α ≈ 0.5979), we demonstrate through a rigorous numerical analysis of 357 galaxies from the SPARC database that Aetheris natively recovers asymptotic flat rotation curves and the exact M ∝ V⁴ slope of the Baryonic Tully-Fisher Relation (BTFR) without requiring dark matter halos. Crucially, this geometric approach uncovers a fundamental topological invariant: g₀ = c · H₀ · (α² · γ). This exact mathematical bridge seamlessly unifies micro-scale galactic dynamics with the macroscopic cosmic expansion rate. Inverting this relation yields a purely analytical prediction for the Hubble constant at H₀ = 69.101 km/s/Mpc, cleanly resolving the Hubble Tension as an optical-geometric illusion. Consequently, the intrinsic cosmological age is calculated at 14.15 Gyr, solving the Methuselah star paradox without the inclusion of Dark Energy. The Aetheris framework mathematically suggests that macroscopic anomalies currently attributed to dark components are dynamic illusions generated by the underlying topological astigmatism of the spacetime vacuum—a geometric distortion that could soon be observationally confirmed by next-generation weak-lensing surveys such as the Euclid mission.